For many applications the relative position and attitude between two platforms has to be known. These applications include the automatic landing of an unmanned aerial vehicle (UAV) on a fixed or moving platform like a ship, pilot assistance for landing, ship docking assistance, and many more. Furthermore, it is also desirable for this information to be available in GNSS (Global Navigation Satellite System)-denied environments. For the sake of simplicity, one of the platforms involved is denoted in the following as ship, the other platform as UAV.
A navigation system capable of providing the required relative position and attitude information consists of four or more transponders onboard the ship and three or more antennas onboard the UAV. The antennas transmit interrogation signals, which are replied by the transponders. These replies are then received by the antennas. The time between transmission of an interrogation signal and the reception of a reply is measured, which allows calculation of the range between antenna and replying transponder.
The Doppler shift of the received signal can also be measured, which can be converted to a measurement of the relative velocity between antenna and transponder. Furthermore, instead of using transponders onboard the ship, synchronized pseudolites can also be used. These pseudolites transmit signals similar to GNSS-signals, which are received by the antennas onboard the UAV. In such a scenario, the UAV does not have to transmit signals, but the range measurements are biased by the offset of the receiver clock, and the Doppler measurements are biased by the frequency error of the receiver clock.
A relative navigation system like described above is discussed in the publication “Stand-Alone Ship-Relative Navigation System Based on Pseudolite Technology”; Aulitzky, C.; Heinzinger, O.; Bestmann, U.; Hecker, P.; “ AIAA Guidance, Navigation, and Control Conference, 10-13 Aug. 2009, Chicago, Ill., USA. In the method presented in this paper, the relative position of each antenna with regard to the ship body frame is estimated using a non-linear least squares approach, and constraints are applied to consider the relative geometry between these antennas. Then, the relative attitude is calculated from the relative antenna positions. This solution has several drawbacks:                The number of unknowns to be estimated grows with the number of antennas.        Doppler measurements cannot be considered.        The range measurements made from all antennas to all transponders/pseudolites must be valid at the same point in time, otherwise systematic errors are introduced. In other words, it is not possible to sequentially perform measurements, i.e. measuring ranges between the first antenna and the transponders/pseudolites, then measuring ranges with the second antenna, and after that measuring ranges with the third antenna. Such an approach provides range measurements with a different time of validity for each antenna. It is a severe drawback that the method described in the above referenced paper introduces systematic errors in such a scenario, because many off-the-shelf range measurement systems exactly operate that way.        The measurements of additional sensors like an inertial measurement unit (IMU), and a radar or laser altimeter cannot be considered easily, which is also a severe drawback.        